IIT JAM Physics flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Divergence of curl

For any twice-differentiable vector field A, div(curl A) = 0 identically. This identity underlies the statement that magnetic field lines have no sources, ∇·B = 0.

Gauss divergence theorem

The outward flux of a vector field through a closed surface equals the volume integral of its divergence: ∮A·dS = ∫(∇·A)dV. It converts surface integrals into volume integrals.

Stokes' theorem

The line integral of a vector field around a closed loop equals the flux of its curl through any surface bounded by the loop: ∮A·dl = ∫(∇×A)·dS.

Parallel-axis theorem

The moment of inertia about any axis equals that about a parallel axis through the centre of mass plus Md², where d is the separation: I = I_cm + Md².

Rolling without slipping

The contact point is instantaneously at rest, so v_cm = ωR. Total kinetic energy is ½mv² + ½Iω², combining translation of the centre of mass and rotation about it.

Angular momentum conservation

If net external torque about an axis is zero, L = Iω stays constant. A skater pulling in her arms reduces I and raises ω so that Iω is unchanged.

Simple pendulum period

For small angular amplitudes, T = 2π√(L/g), independent of mass. For a physical pendulum the same form holds with L replaced by I/(md).

Damped oscillator frequency

With damping force −bv, the amplitude decays as e^(−bt/2m) and the angular frequency becomes ω′ = √(ω₀² − b²/4m²), slightly below the undamped ω₀.

Resonance condition

A driven oscillator attains maximum amplitude when the driving frequency equals the natural frequency ω₀ = √(k/m). At resonance the amplitude is limited only by damping.

String wave speed

Transverse waves on a stretched string travel at v = √(T/μ), where T is tension and μ is linear mass density. Higher tension raises speed; a heavier string lowers it.

Closed pipe harmonics

A pipe closed at one end supports only odd harmonics: f_n = (2n−1)v/(4L). The fundamental has a node at the closed end and an antinode at the open end.

Doppler effect formula

f′ = f(v ± v_o)/(v ∓ v_s). The numerator takes + when the observer approaches the source; the denominator takes − when the source approaches the observer.

Beats frequency

Two superposed waves of nearby frequencies f₁ and f₂ produce an amplitude that waxes and wanes at the beat frequency |f₁ − f₂|, heard as loudness pulsations.

First law of thermodynamics

ΔU = Q − W, where W is the work done by the system. In an isochoric process W = 0, so all heat supplied goes into raising internal energy.

Adiabatic process relation

For a reversible adiabatic process in an ideal gas, PV^γ = constant, with γ = C_p/C_v. No heat is exchanged, so work done comes entirely from internal energy.

Carnot efficiency

The maximum efficiency of a heat engine operating between reservoirs at T_h and T_c is η = 1 − T_c/T_h, with temperatures in kelvin. No real engine between the same reservoirs can exceed this.

Mean free path

The average distance a gas molecule travels between collisions is λ = 1/(√2 π d² n), where d is molecular diameter and n is number density. It grows as pressure falls.

Equipartition theorem

Each quadratic degree of freedom contributes ½k_BT per molecule to the mean energy. A monatomic gas has three translational degrees, giving C_v = (3/2)R.

Clausius inequality

For any cyclic process, ∮dQ/T ≤ 0, with equality only for reversible cycles. It leads directly to the entropy statement of the second law.

Entropy change in free expansion

An ideal gas expanding into vacuum at constant temperature has ΔS = nR ln(V₂/V₁) > 0, even though no heat enters and no work is done.

Lorentz factor

γ = 1/√(1 − v²/c²) ≥ 1. It measures the departure from Newtonian kinematics and appears in time dilation, length contraction, and relativistic momentum.

Time dilation

A clock moving at speed v relative to an observer runs slow: Δt = γΔτ, where Δτ is the proper time measured in the clock's rest frame. Verified by muon lifetimes.

Relativistic energy-momentum relation

E² = (pc)² + (m₀c²)². For a photon m₀ = 0, giving E = pc; for a particle at rest, E = m₀c².

Photoelectric threshold

Electrons are emitted only when hν exceeds the work function φ. Maximum kinetic energy is K_max = hν − φ, and the stopping potential satisfies eV₀ = K_max.

de Broglie wavelength

A particle of momentum p has wavelength λ = h/p. For an electron accelerated through potential V, λ ≈ 12.27/√V Å, which is why electron diffraction is observable.

Bohr energy levels

Hydrogen levels are E_n = −13.6 eV/n². The Lyman series ends on n = 1 (ultraviolet), Balmer on n = 2 (visible), and Paschen on n = 3 (infrared).

Heisenberg uncertainty relation

Δx·Δp ≥ ħ/2 for position and momentum, and ΔE·Δt ≥ ħ/2 for energy and time. These are statistical spreads, not measurement disturbances.

Radioactive decay law

N = N₀e^(−λt); the half-life is t₁/₂ = ln2/λ ≈ 0.693/λ, and the mean lifetime is 1/λ. Activity A = λN also falls exponentially.

Mass defect and binding energy

The binding energy of a nucleus is B = [Zm_p + (A−Z)m_n − M]c². It peaks near iron-56, so fusion releases energy for light nuclei and fission for heavy ones.

Lens formula and magnification

Thin lens: 1/f = 1/v − 1/u with sign conventions; transverse magnification m = v/u. For a simple microscope, angular magnification is D/f for image at infinity.

Young double-slit fringe width

Fringe spacing is β = λD/d, where D is the screen distance and d the slit separation. It increases with wavelength and screen distance, and decreases with slit separation.

Single-slit diffraction minima

Minima occur at a sinθ = nλ for slit width a. The central maximum spans twice the width of the secondary maxima and is much brighter.